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Perturbation methods for Markov-switching DSGE models

Author

Listed:
  • Foerster, Andrew

    () (Federal Reserve Bank of Atlanta)

  • Rubio-Ramírez, Juan

    () (Duke University)

  • Waggoner, Daniel F.

    () (Federal Reserve Bank of Atlanta)

  • Zha, Tao

    ()

Abstract

This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of Markov-switching DSGE models. We introduce an important and practical idea of partitioning the Markov-switching parameter space so that a steady state is well defined. With this definition, we show that the problem of finding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Grobner bases in searching all the solutions to the quadratic system. This approach allows us to obtain all the approximations and ascertain how many of them are stable. Our methodology is applied to three models to illustrate its feasibility and practicality.

Suggested Citation

  • Foerster, Andrew & Rubio-Ramírez, Juan & Waggoner, Daniel F. & Zha, Tao, 2013. "Perturbation methods for Markov-switching DSGE models," FRB Atlanta Working Paper 2013-01, Federal Reserve Bank of Atlanta.
  • Handle: RePEc:fip:fedawp:2013-01
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    File URL: http://www.frbatlanta.org/documents/pubs/wp/wp1301.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Markov-switching parameters; partition; higher order approximations; no certainty equivalence; quadratic system; Grobner bases;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

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